This renewal proposal requests funding to continue the development and offering of short courses focusing on the mathematical and computational methods necessary to analyze biological complexity. We will build upon the success of the prior course offerings to develop and present three short courses over one year. Each short course will be four days in length and will include workshop sessions as well as formal lectures and interactive discussion sections. The overall objective of these short courses is to provide sufficient background that the participants will be able to read with understanding the computationally and quantitatively oriented literature in their area of biology. Additionally, the short courses will provide an entree to the training needed to actually carry out research using these techniques. The first course will provide an overview of mathematical and computational approaches including continuous and discrete dynamical systems, and stochastic models. This will repeat and supplement one of the short courses offered under the prior award. The second course will focus on the application of optimal control theory to biological problems, particularly related to drug usage, disease, cancer and bioreactor models. The third course will focus on modeling the genetic basis of complex phenotypes, covering various theoretical approaches used to model traits that are complex either because they have an inherently complex genetic basis (e.g. determined by large numbers of genes or with complex pleiotropy) or because they are influenced by genetic factors that are conceptually complex (e.g. epistasis).